Proposal of finite element analysis method for dielectric breakdown based on Maxwell’s equations

Abstract

This paper proposes a new approach to the simulation of discharge phenomena in dielectric breakdown including field fluctuations based on Maxwell’s equations in the finite element framework without introducing the artificial stochastic disturbance. This method is based on the idea that field fluctuations caused by the development of electrical treeing propagates as electromagnetic wave governed by Maxwell’s equations, and triggers next dielectric breakdown in a chain reaction. The obtained model can be regarded as the equivalent circuit model in which the resistors representing local property of material are arranged. The key point of the proposed method is the ease of expressing dielectric breakdown as replacement of the arranged resistors. Dielectric breakdown expressed as the local change of conductivity leads to the inhomogeneity of the conductivity. In addition to this simplest model for dielectric breakdown, constraint on the discharge paths to the finite edges in the circuit is applied. This corresponds to the introduction of the implicit inhomogeneity. This implicit inhomogeneity plays a significant role in the process of formation of branching discharge patterns. The capability of introduction of the implicit inhomogeneity and the constraint on the possible candidates for propagation paths enable the proposed method to find out a bifurcated solution and make it easier to analyze formation of discharge patterns in dielectric breakdown. This paper explains these features of the proposed mathematical model with results of numerical simulation of several example problems.